next up previous contents
Next: 3.5 Logarithmus, Hauptwert, Up: 3. Die Dirac'sche -Funktion Previous: 3.3 Formeln mit   Inhalt

3.4 Dreidimensionale $ \delta$-Funktion


$\displaystyle \delta$($\displaystyle \vec{x}\,$-$\displaystyle \vec{x'}\,$)=$\displaystyle \delta$(x1-x1')$\displaystyle \delta$(x2-x2')$\displaystyle \delta$(x3-x3')=
$\displaystyle {{1 \over r^2}\delta(r-r') \delta(\cos(\theta)- \cos(\theta')) \delta(\varphi- \varphi') =}$
$\displaystyle {-{1 \over {4 \pi}} \Delta {1 \over {\vert\vec{x}-\vec{x'}\vert}}}$

$\displaystyle \vec{x}\,$ = (x1, x2, x3) (3.15)

bzw. in Kugelkoordinaten

$\displaystyle \vec{x}\,$ = (rcos($\displaystyle \varphi$)sin($\displaystyle \theta$), rsin($\displaystyle \varphi$)sin($\displaystyle \theta$), rcos($\displaystyle \theta$)) (3.16)


Alexander Wagner
2000-04-14